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Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

4
votes
2answers
I want to solve a system of nonlinear two differential equations (say, in $\theta(x,t)$ and $\phi(x,t)$ with NDSolve, but I want to stop the evaluation when one of the functions ($\phi(x,t)$) reaches …
asked Mar 20 '14 by usumdelphini
2
votes
0answers
At some point I get this error: Warning: scaled local spatial error estimate of 32773.0090044258` at t = 987.7919550194803` in the direction of independent variable x is much greater than the …
asked Apr 1 '14 by usumdelphini
1
vote
2answers
I am trying to solve the following nonlinear ODE, but Mathematica takes forever to give a result. Any idea why? eq = f''[r] + r^-1 f'[r] - r^-2 f[r] + (1 - r^2) f[r] == 0 g[r_] = f[r] /. NDSolve[{e …
asked Jan 19 '16 by usumdelphini
2
votes
2answers
I was wondering if one could define an operator such that, when I give a certain number of (differential) equations as an output, and an "equilibrium" value for each of the variables, it returns the l …
asked Mar 2 '15 by usumdelphini
0
votes
0answers
NDsolve gives me a solution to a certain NL PDE. I want to evaluate the rate of exponential decay of the maxima of the solutions in time. So, I plot Max1[t_?NumericQ] := First[Maximize[sol1[[1]][x, t …
asked Nov 18 '13 by usumdelphini
0
votes
0answers
I solve a NonLinear PDE and get a solution (which for other reasons I put into a vector): SolVec1[1][[2]][x,t], where x and t are the indipendent variables. Now, I would like to get a distribution o …
asked Feb 16 '14 by usumdelphini
3
votes
1answer
I am solving Laplace equation with particular geometry and boundary conditions: L = 10; a = 1; k = 1/2; mesh = 0.06; BoxL = x == L || x == -L || y == L || y == -L; reg = ImplicitRegion[(-L <= x <= …
asked Mar 30 '15 by usumdelphini